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Historical records show that there was no real concept of probability in Europe before the mid-seventeenth century, although the use of dice and other randomizing objects was commonplace. Ian Hacking presents a philosophical critique of early ideas about probability, induction, and statistical inference and the growth of this new family of ideas in the fifteenth, sixteenth, and seventeenth centuries. Hacking invokes a wide intellectual framework involving the growth of science, economics, and the theology of the period. He argues that the transformations that made it possible for probability concepts to emerge have constrained all subsequent development of probability theory and determine the space within which philosophical debate on the subject is still conducted. First published in 1975, this edition includes an introduction that contextualizes his book in light of developing philosophical trends. Ian Hacking is the winner of the Holberg International Memorial Prize 2009.

Philosophy of science --- Probabilities --- Induction (Mathematics) --- Mathematical statistics --- History. --- Arts and Humanities --- Philosophy --- Induction (Logic) --- Mathematics --- Mathematical induction --- Probabilités --- Induction (mathématiques) --- Statistique mathématique --- Histoire --- History

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"Induction is a pervasive tool in computer science and mathematics for defining objects and reasoning on them. Coinduction is the dual of induction and as such it brings in quite different tools. Today, it is widely used in computer science, but also in other fields, including artificial intelligence, cognitive science, mathematics, modal logics, philosophy and physics. The best known instance of coinduction is bisimulation, mainly employed to define and prove equalities among potentially infinite objects: processes, streams, non-well-founded sets, etc. This book presents bisimulation and coinduction: the fundamental concepts and techniques and the duality with induction. Each chapter contains exercises and selected solutions, enabling students to connect theory with practice. A special emphasis is placed on bisimulation as a behavioural equivalence for processes. Thus the book serves as an introduction to models for expressing processes (such as process calculi) and to the associated techniques of operational and algebraic analysis"--

Bisimulation. --- Coinduction (Mathematics) --- Modality (Logic) --- Induction (Mathematics) --- Computer science. --- Informatics --- Science --- Mathematical induction --- Induction (Logic) --- Mathematics --- Modal logic --- Logic --- Nonclassical mathematical logic --- Bisimulation --- Mathematical coinduction

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681.3*I23 --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- Artificial intelligence. Robotics. Simulation. Graphics --- Mathematical logic --- Artificial intelligence. --- Logic, Symbolic and mathematical.

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Description Logics are embodied in several knowledge-based systems and are used to develop various real-life applications. The Description Logic Handbook provides a thorough account of the subject, covering all aspects of research in this field, namely theory, implementation, and applications. Its appeal will be broad, ranging from more theoretically-oriented readers, to those with more practically-oriented interests who need a sound and modern understanding of knowledge representation systems based on Description Logics. As well as general revision throughout the book, this new edition presents a new chapter on ontology languages for the semantic web, an area of great importance for the future development of the web. In sum, the book will serve as a unique reference for the subject, and can also be used for self-study or in conjunction with Knowledge Representation and Artificial Intelligence courses.

681.3*F4 --- 681.3*H1 --- 681.3*I23 --- Description logics --- Logics, Description --- Knowledge representation (Information theory) --- Predicate (Logic) --- Mathematical logic and formal languages (Theory of computation) --- Models and principles (Information systems) --- Deduction and theorem proving: answer/reason extraction reasoning resolution metatheory mathematical induction logic programming (Artificial intelligence) --- 681.3*H1 Models and principles (Information systems) --- 681.3*F4 Mathematical logic and formal languages (Theory of computation) --- 681.3*I23 Deduction and theorem proving: answer/reason extraction reasoning resolution metatheory mathematical induction logic programming (Artificial intelligence) --- Logiques de description --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- Description logics - Handbooks, manuals, etc.

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Geared to preparing students to make the transition from solving problems to proving theorems, this text teachs them the techniques needed to read and write proofs. The book begins with the basic concepts of logic and set theory, to familiarize students with the language of mathematics and how it is interpreted. These concepts are used as the basis for a step-by-step breakdown of the most important techniques used in constructing proofs. To help students construct their own proofs, this new edition contains over 200 new exercises, selected solutions, and an introduction to Proof Designer software. No background beyond standard high school mathematics is assumed. Previous Edition Hb (1994) 0-521-44116-1 Previous Edition Pb (1994) 0-521-44663-5

Mathematical logic --- Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- 681.3*I23 Deduction and theorem proving: answer/reason extraction; reasoning; resolution; metatheory; mathematical induction; logic programming (Artificial intelligence) --- Logic, Symbolic and mathematical --- Mathematics --- 681.3*I23 --- Math --- Science --- Algebra of logic --- Logic, Universal --- Symbolic and mathematical logic --- Symbolic logic --- Algebra, Abstract --- Metamathematics --- Set theory --- Syllogism --- Logic, symbolic and mathematical --- Logic, Symbolic and mathematical. --- Mathematics. --- Logique symbolique et mathématique --- Mathématiques